## Abstract

In this paper, we propose an analytic tool for describing the mathematics made available to learn in a ‘textbook lesson’. The tool is an adaptation of the Mathematics Discourse in Instruction (MDI) analytic tool that we developed to analyze what is made available to learn in teachers’ lessons. Our motivation to adapt the use of the MDI analytic framework to textbooks is to test the relative robustness of the framework in moving across different pedagogic texts (e.g. video of a lesson, a textbook lesson). Our initial findings suggest it has applicability across pedagogic texts, thus opening possibilities for using a common framework and language in research and in professional development activities involving the written and enacted curricula.

This is a preview of subscription content, log in to check access.

## Notes

- 1.
Trends in Mathematics and Science Study

- 2.
Further detail on WMCS is available at www.wits.ac.za/WitsMathsConnect.

- 3.
Notice that the word

*examples*here is not the same as they way we define example in the analytic tool described in the previous section. - 4.
- 5.
We acknowledge the resonances here with Stacey & Vincent’s (2009) description of explanation in textbooks in terms of seven ‘modes of reasoning’, particularly in relation to the categories of authority, empirical arguments and generality. Our simpler categorization is a function of our purposes to examine opportunities to learn more comprehensively, and thus for a relatively simple categorization within each of our elements of MDI. Indeed there are resonances here too with endorsement as an element of Sfard’s (2008) theorization of mathematical discourse. Further work in the field that combines these, recognizing the different empirical grounds from which descriptions of substantiation in school mathematics have been developed is a task to take forward.

## References

Adler, J. (1999). The dilemma of transparency: Seeing and seeing through talk in the mathematics classroom.

*Journal for Research in Mathematics Education, 30*(1), 47–64.Adler, J. (2000). Conceptualising resources as a theme for mathematics teacher education.

*The Journal of Mathematics Teacher Education, 3*(3), 205–224.Adler, J. (2001).

*Teaching mathematics in multilingual classrooms.*Dordrecht, Netherlands: Kluwer Academic.Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education.

*Journal for Research in Mathematics Education, 37*(4), 270–296.Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching.

*African Journal of Research in Mathematics, Science and Technology Education, 19*(3), 237–254. doi:10.1080/10288457.2015.1089677.Adler, J., & Ronda, E. (2016). Mathematical discourse in instruction matters. In J. Adler & A. Sfard (Eds.), Research for educational change: Transforming researchers’ insights into improvement in mathematics teaching and learning. Abingdon, England: Routledge (in press).

Adler, J., & Venkat, H. (2014). Teachers’ mathematical discourse in instruction: Focus on examples and explanations. In M. Rollnick, H. Venkat, M. Askew, & J. Loughran (Eds.),

*Exploring content knowledge for teaching science and mathematics.*London, England: Routledge.Askew, M., Hodgen, J., Hossain, S. & Bretscher, N. (2010).

*Values and variables: Mathematics education in high-performing countries*. London, England: Nuffield.Bernstein, B. B. (2000).

*Pedagogy, symbolic control, and identity: Theory, research, critique (Revised ed.)*. Lanham, MD: Rowman & Littlefield.Bowie, L. (2013).

*The constitution of school geometry in the Mathematics National Curriculum Statement and two Grade 10 geomtery textbooks in South Africa*(Unpublished doctoral dissertation). Johannesburg, South Africa: University of the Witwatersrand.de Freitas, E., Wagner, D., Esmonde, I., Knipping, C., Lunney Borden, L. & Reid, D. (2012). Discursive authority and sociocultural positioning in the mathematics classroom: New directions for teacher professional development.

*Canadian Journal of Science, Mathematics, and Technology Education, 12*(2), 137–159. doi:10.1080/14926156.2012.679994.Dole, S. & Shield, M. (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning.

*Research in Mathematics Education, 10*(1), 19–35.Dolev, S. & Even, R. (2013). Justifications and explanations in Israeli 7th grade math textbooks.

*International Journal of Science and Mathematics Education, 13*(Suppl. 2), 1–19. doi:10.1007/s10763-013-9488-7.Fan, L., Zhu, Y. & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions.

*ZDM, 45*(5), 633–646.Fleisch, B., Taylor, N., Herholdt, R. & Sapire, I. (2011). Evaluation of Back to Basics mathematics workbooks: A randomised control trial of the Primary Mathematics Research Project.

*African Journal of Education, 31*, 488–504.Leshota, M. (2015).

*The relationship between textbooks affordances and teachers' pedagogical design capacity*(Unpublished doctoral dissertation). Johannesburg, South Africa: University of the Witwatersrand.Lo, M. (2012).

*Variation theory and the improvement of teaching and learning*. Retrieved from https://gupea.ub.gu.se.Marton, F. & Pang, M. F. (2006). On some necessary conditions of learning.

*The Journal of the Learning Sciences, 15*(2), 193–220.Marton, F. & Tsui, A. B. M. (2004).

*Classroom discourse and the space of learning*. Mahwah, NJ: Erlbaum.Nagao, M., Rogan, J. & Magno, M. (2007).

*Mathematics and science education in developing countries: Issues, experiences, and cooperation prospects*. Quezon City, Philippines: UP Press.Newton, J. (2012). Investigating the mathematical equivalence of written and enacted middle school standards-based curricula: Focus on rational numbers.

*International Journal of Educational Research, 51*, 66–85.Pimm, D. & Wagner, D. (2003). Investigation, mathematics education and genre: An essay review of Candia Morgan’s writing mathematically: The discourse of investigation.

*Educational Studies in Mathematics, 53*, 159–178.Reys, B. J., Reys, R. E. & Koyama, M. (1996). The development of computation in three Japanese primary-grade textbooks.

*The Elementary School Journal, 96*(4), 423–437.Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review.

*Reading & Writing Quarterly, 23*(2), 139–159. doi:10.1080/10573560601158461.Sfard, A. (2008).

*Thinking as communication*. Cambridge, England: Cambridge University Press.Shield, M. & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning.

*Educational Studies in Mathematics, 82*(2), 183–199.Stacey, K. & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks.

*Educational Studies in Mathematics, 72*(3), 271–288.Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks.

*Mathematical Thinking and Learning, 11*(4), 258–288.Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H. & Houang, R. T. (2002).

*According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks*. Dordrecht, The Netherlands: Kluwer.Venkat, H., & Adler, J. (2012). Coherence and connections in teachers' mathematical discourses in instruction.

*Pythagoras, 33*(3), 1–8.Vygotsky, L. S. (1978).

*Mind in society: The development of higher psychological processes*. Cambridge, England: Harvard University Press.Wagner, D. (2015). A speech act in mathematics education: The social turn. In P. Gates & R. J. Zevenbergen (Eds.),

*Shifts in the field of mathematics*. Singapore: Springer Science+Business Media.Yang, K. (2013). A framework for analysing textbooks based on the notion of abstraction.

*For the Learning of Mathematics, 33*(1), 31–37.Zodik, I. & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom.

*Educational Studies in Mathematics, 69*(2), 165–182. doi:10.1007/s10649-008-9140-6.

## Author information

### Affiliations

### Corresponding author

## Rights and permissions

## About this article

### Cite this article

Ronda, E., Adler, J. Mining Mathematics in Textbook Lessons.
*Int J of Sci and Math Educ* **15, **1097–1114 (2017). https://doi.org/10.1007/s10763-016-9738-6

Received:

Accepted:

Published:

Issue Date:

### Keywords

- Analytic framework
- Curriculum studies
- Mathematics discourse
- Opportunities to learn
- Socio-cultural theory
- Textbooks studies